Technical Notes on Mars Solar Time as Adopted by the Mars24 Sunclock
(Updated June 30, 2015)
These notes provide a technical brief on the definitions of numeric readouts in Mars24. Further details can be found in the references, chiefly the two articles by Allison (1997) and by Allison and McEwen (2000). A less technical account of solar time on Mars is provided in the 1998 article "Telling Time on Mars" on the NASA GISS website. Information about the specific controls and displays in Mars24 is provided in the accompanying User's Guide.
Mars Solar Days and 24-hr Clock Convention
Following the long-standing practice originally adopted in 1976 by the Viking Lander missions, the daily variation of Mars solar time is reckoned in terms of a "24-hour" clock, representing a 24-part division of the planet's solar day, along with the traditional sexagesimal subdivisions of 60 minutes and 60 seconds. A Mars solar day has a mean period of 24 hours 39 minutes 35.244 seconds, and is customarily referred to as a "sol" in order to distinguish this from the roughly 3% shorter solar day on Earth. The Mars sidereal day, as measured with respect to the fixed stars, is 24h 37m 22.663s, as compared with 23h 56m 04.0905s for Earth.
Mars Solar Seasons
The apparent seasonal advance of the Sun at Mars is commonly measured in terms of the areocentric longitude Ls, as referred to the planet's vernal equinox (the ascending node of the apparent seasonal motion of the Sun on the planet's equator). As defined, Ls = 0°, 90°, 180°, and 270° indicate the Mars northern hemisphere vernal equinox, summer solstice, autumnal equinox, and winter solstice, respectively.
In terms of Ls, the seasonally variable, planet-centered solar declination d equals arcsin [(sin ε)(sin Ls)], where the obliquity ε is the inclination of the planet's spin axis with respect to the plane of its orbit. For an accurate account of the solar illumination relative to the plane of a locally flat surface, the solar declination can be corrected for the small difference appropriate to the so-called planetographic measure of latitude on an oblate sphere, as it is in the Mars24 sunclock.
As a result of the Mars's orbital eccentricity, Ls advances somewhat unevenly with time, but can be efficiently evaluated as a trigonometric power series for the orbital eccentricity and the orbital mean anomaly measured with respect to the perihelion. The areocentric longitude at perihelion, Ls,p = 251°.000 + 0°.0064891×(yr - 2000), indicates a near alignment of the planet's closest approach to the Sun in its orbit with its winter solstice season, as related to the occasional onset of global dust storms within the advance of this season.
Mars Orbit Periods
The period for the repetition of the planet-centered measure of mean Solar longitude is referred to as the tropical year. (This period is linked to the rate of advance of the "Fictitious Mean Sun," as discussed below.) The Mars tropical year is 686.9725 day or 668.5921 sol. For comparison, the Mars sidereal year, as measured with respect to the fixed stars, is 668.5991 sol. The difference between these values results from the precession of the planet's spin axis.
The mean interval between the repetition of the planet's perihelion passage, or anomalistic year, is 668.6147 sol, and corresponds to the rate of advance of the planet's orbital mean anomaly. The mean repetition period for a particular solar season varies with the Ls. The mean repetition intervals for the vernal equinox, summer solstice, autumnal equinox, and winter solstice on Mars are 668.5906 sol, 668.5879 sol, 668.5940 sol, and 668.5957 sol, respectively, and the average of these is just the tropical year.
Mean and True Solar Time
Also as a result of a planet's orbital eccentricity, as well as its obliquity, there is a seasonally variable discrepancy between the even advance of an artificially defined Mean Solar Time and of the True Solar Time corresponding to the actual planet-centered position of the Sun in its sky. Following the conventional usage of terrestrial timekeeping, Mean Solar Time on Mars has been defined in reference to the so-called Right Ascension of the Fictitious Mean Sun (FMS). As defined, the FMS is the angle between the planet's vernal equinox, measured along the plane of its equator, and an artificially defined "dynamical mean Sun" advancing at a rate corresponding to the planet's solar tropical year (i.e., the Mars FMS advances at a rate of 360°/686.9725 day or 0.5240384°/day). Its numerical value (to within an arbitrary multiple of 360°) is just the sum of the orbital mean anomaly, M, and the areocentric longitude at perihelion, Ls,p. The FMS at Mars was evaluated by Allison and McEwen (2000) (hereafter "AM2000") as a mean fit to an accurate calculation of the areocentric longitude over 134 Mars orbits (for the years 1874-2127), adjusted in its angular placement by the (~0°.0046) solar aberration. This evaluation has been adopted by the Mars Exploration Rover project for its definition of Mars Mean Solar Time (cf. Roncoli et al., 2002).
The difference between the True Solar Time (TST) and the Mean Solar Time (MST), equivalent in the corresponding angular measure to the difference between the right ascensions of the FMS and the true Sun, is referred to as the Equation of Time (EOT). For Earth, the EOT varies between -14.2min and +16.3min. Mars, with its more than five times larger orbital eccentricity, has an EOT varying between -51.1min and +39.9min. The parametric plot of the EOT vs. the solar declination is called the solar analemma. For Earth, this takes the form of the figure-8 pattern marked on some sundials and globes (for the latter typically in the empty space of the South Pacific). For Mars, the analemma assumes the shape of a raindrop or mis-shapen pear.
Local and "Zonal" Times
The definition of the Mars prime meridian has become more refined as observations of the planet have allowed its improvement. A small circular feature observed in the 1830s by astronomers attempting to measure the planet's rotation was used in 1877 to designate longitude 0°. The location was subsequently named Sinus Meridiani. Following observations of Mars by the Mariner 9 probe, a half-kilometer wide crater within Sinus Meridiani was used to designate longitude 0° (de Vaucoulers et al., 1973). The crater was later named Airy-0 in honor of the British astronomer George Biddel Airy, who built the telescope at Greenwich whose location defined the prime meridian on Earth. A recent effort to constrain the uncertainty in Mars lander locations has suggested a further refinement of the prime meridian definition to within 6 meters based on the lander locations, and specifically that longitude 0° be exactly 47.95137° east of Viking Lander 1 (Kuchynka, 2014).
The Mars24 application refers to mean solar time at Mars's prime meridian as "Airy Mean Time" (AMT), in analogy to Earth's "Greenwich Mean Time" (GMT), although the latter term has been supplanted by the more accurate Coordinated Universal Time (UTC) in international timekeeping services.
For a given location on Mars, the Local True Solar Time (LTST) and Local Mean Solar Time (LMST) are easily determined from the TST and MST at the prime meridian by adding a number of Mars hours equal to the location's east longitude divided by 15. Thus, a location at 45°W would have an LTST that is exactly three Mars hours behind the true solar time at 0°.
In the mid-1800s the use of locally measured and defined time on Earth was gradually supplanted by the use of time zones in order to facilitate standardization of railroad schedules and, to a lesser extent, of recording scientific observations. This process culminated in 1884 in an international conference that created the global system of time zones and specified the longitude of Greenwich as the prime meridian. Each zone is approximately 15° wide, the exact width and shape subject to political boundaries and significant geographic features. Within each, zone clocks are referenced to the same hour.
Mars24 includes the option to display the local time at a selected location in terms of similarly constructed "Mars time zones". We have defined these Mars time zones to be exactly 15° wide and centered on successive 15° multiples of longitude, at 0°, 15°, 30°, etc. We have not attempted to name these time zones, as for example "Olympus Standard Time", but do identify their read-out with a suffix indicating the timezone offset. Thus, for the the case of Olympus Mons the timezone identifier is "AMT-9", or nine Mars hours behind Airy Mean Time.
Mars Sol Date (MSD)
Although numerous month-year calendars have been proposed for Mars, we have not attempted to support any of these as a feature of Mars24. We have, however, included in the Mars24 displays the "Mars Sol Date" (MSD) defined by AM2000. This represents a sequential count of Mars solar days elapsed since 1873 December 29 at approximately Greenwich noon (Julian Date 2405522.0). This epoch was prior to the great 1877 perihelic opposition of Mars and precedes nearly all detailed observations of temporal changes on the planet. It corresponds to a Mars Ls of 277°, approximately the same planetocentric solar longitude as that for the Earth on the same date. MSD 44796.0 is approximately coincident with 2000 January 6.0, at a near-coincidence of prime meridian midnights on the two planets and a repetition of Mars Ls = 277°. The period 44796 sols also represents a near commensurability of 126 Julian years and 67 Mars tropical revolutions. In principle, the MSD could be used as a coherent sol-date reference for a variety of Mars missions.
Mars24 uses the short-series representation of the seven-largest short-period planetary perturbations of the Mars orbital longitude specified by AM2000, as adapted from Simon et al. (1994). Detailed comparisons with an accurate ephemeris suggest that the maximum error in the calculated Ls by the adopted algorithm is 0°.008 over ±100 years of J2000. According to the implicit dependence of the calculated EOT on the Ls, the resulting True Solar Time can be estimated to be in error by as much as 3 sec. The error in the currently coded conversion between TT and UTC is itself in error for some periods in the post-1975 era by as much as 3 sec.
Of course, the calculation of local (true or mean) solar time cannot be any more accurate than the longitudinal placement of the local point of interest. Predicted solar times for a given lander location may therefore need to be revised as improved knowledge of their locations becomes available. Although relatively precise coordinates of post-2000 landers were obtained quickly after their landing, disputes as to the precise locations of the two Viking Landers continued for some time and were not settled until the landers were spotted in surface photography taken by later orbiters.
Although time-of-day may be calculate from knowledge of longitude, estimates of the times of local sunrise and sunset, as well as times of Earthrise and Earthset, also require the latitude. Even so, the results may be in error due to local topography and atmospheric refraction. Comparison to known times for a limited number of solar and Earth rise and set events at Mars lander sites suggest that absent topographic and atmospheric effects, the error in calculating these times is less than 30 seconds.
Lander Mission Times
Each Mars lander mission project has adopted a different reference for its solar timekeeping and mission clock. Mission dates are commonly given as a count of sols since the date on which the particular lander touched down on the Martian surface. Depending on mission criteria, the sol during which landing occurred has been variously designated as either Sol 0 or Sol 1. A second question has been how to define the epoch when the initial sol commenced, and again this has varied, being based on either the (planned) landing site LTST or LMST midnight immediately prior to the landing, or on some specified offset from that prior midnight. But no matter how this initial epoch for the mission clock has been defined, all but one of the lander clocks have then "ticked away" at a rate of mean Mars time.
Note: For the earlier lander missions — the two Viking Landers as well as Mars Pathfinder — discrepancies between mission clock specifications and Mars24's attempt to match mission data timetags are the result of improved knowledge of the Mars spin pole as well as updates to Martian cartography, both arising from data collected by these missions as well as from photography collected by orbiter missions such as the Viking Orbiters and Mars Global Surveyor.
Viking Landers (VL1, VL2): The "local lander time" for each of the two Viking Lander missions began with Sol 0, in each case commencing from midnight LTST at the respective lander location immediately prior to touchdown, but advancing at the rate of mean solar time. The locations used in determining the LTST midnight were apparently the landing coordinates selected during the period between when the Viking Orbiters reached Mars and when the Landers were deployed, i.e., the longitude used for VL1 time calculations was 312.5°E and for VL2 was 134.14°E. However, Mars24 uses explicit UTC epochs for each Viking Lander's Sol 0 that were obtained from lander meteorology tape documentation archived with the National Space Science Data Center.
Pathfinder (MPF): Mission planning documentation for the Mars Pathfinder lander and its Sojourner rover discussed not only the meaning of LTST and LMST but also a "hybrid solar time", essentially a somewhat complex offset version of LMST that would have been periodically adjusted to constrain the difference between LTST and the offset LMST to less than 5 min (Vaughan, 1995). However, timetags for the "Mars local solar time" included in material such as the Pathfinder mission website (e.g., the trajectory data webpage) all appear to have used only a LTST schema rather than the hybrid system. The Mars24 display of MPF mission time uses LTST timekeeping and is intended to match these posted timetags.
Mars Exploration Rovers (MER-A, MER-B): The "local solar time" adopted for the Mars Exploration Rover Project was based on an offset from landing site LMST as described by Roncoli et al. (2002). The intention of these offsets was that at approximately the middle of each of the MER-A and -B nominal missions (i.e., on the 45th sol after landing), lander mission time should align with LTST to within 30 seconds. For MER-A Spirit, the difference between lander mission time and LMST was more than 41 minutes; while for MER-B Opportunity the difference is more than 37 minutes. As with Pathfinder, Sol 1 for each MER lander denoted the solar day on which the lander touched down. Although based on the planned landing longitudes, the clock times for both rovers are calculated in Mars24 using explicit UTC epochs.
Phoenix (PHX): The Mars Phoenix mission reverted to using Sol 0 to indicate the solar day on which the lander touched down. Mission controllers originally specified a mission clock based on the LMST at a planned landing site at 233.35°E. However, there was a late decision to shift the landing about 0.9° eastward, while retaining a mission clock based on the prior location. Thus, mission time specified that the Sol 0 epoch would start at midnight LMST at 233.35°E prior to landing. This decision would have resulted in a mission clock offset from LMST by about two and half minutes, but as it turned out, Phoenix landed 5 km off target, at 234.24845°E. The end result was that mission time and lander site LMST differed by about three and a half minutes.
Mars Science Laboratory (MSL): The Mars Science Laboratory rover project also defined Sol 0 as the solar day on which the lander would touch down. During planning, mission controllers specified a mission clock commencing at midnight LMST for a landing site at 137.42°E. The landing site was later slightly altered and course corrections were made while MSL was in-flight to Mars. As the rover, Curiosity, landed slightly "long" of the final target coordinates, the landing site turned out to be at 137.441635°E. Following the example of Phoenix, there was no re-definition of the MSL mission clock to match the actual landing coordinates, and so a difference of a several seconds between LMST at the landing site and mission clock resulted.